This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070832 #36 Aug 14 2025 03:13:22
%S A070832 1,2,12872,1470944,622116992,125858012672,36758056208384,
%T A070832 8793364151263232,2334899414608412672,586347560750962049024,
%U A070832 151652224498623981289472,38612725801339748322639872,9913426188311626771400228864
%N A070832 a(n) = Sum_{k=0..n} binomial(8*n,8*k).
%H A070832 Seiichi Manyama, <a href="/A070832/b070832.txt">Table of n, a(n) for n = 0..415</a>
%H A070832 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (136,32880,-552704,-65536).
%F A070832 Let b(n) = a(n)-2^(8*n)/8 then b(n)+120*b(n-1)-2160*b(n-2)-256*b(n-3)=0. - _Benoit Cloitre_, May 27 2004
%F A070832 a(n) = 1/4*16^n + 1/8*256^n + 1/4*(-68 + 48*sqrt(2))^n + 1/4*(-68-48*sqrt(2))^n.
%F A070832 From _Colin Barker_, May 27 2019: (Start)
%F A070832 G.f.: (1 - 134*x - 20280*x^2 + 207296*x^3 + 8192*x^4) / ((1 - 16*x)*(1 - 256*x)*(1 + 136*x + 16*x^2)).
%F A070832 a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>4.
%F A070832 (End)
%t A070832 Table[Sum[Binomial[8n,8k],{k,0,n}],{n,0,15}] (* _Harvey P. Dale_, Nov 25 2020 *)
%o A070832 (PARI) a(n)=sum(k=0,n,binomial(8*n,8*k)); \\ _Benoit Cloitre_, May 27 2004
%o A070832 (PARI) Vec((1 - 134*x - 20280*x^2 + 207296*x^3 + 8192*x^4) / ((1 - 16*x)*(1 - 256*x)*(1 + 136*x + 16*x^2)) + O(x^15)) \\ _Colin Barker_, May 27 2019
%Y A070832 Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), A070782 (b=5), A070967 (b=6), A094211 (b=7), this sequence (b=8), A094213 (b=9), A070833 (b=10).
%K A070832 easy,nonn
%O A070832 0,2
%A A070832 Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002
%E A070832 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 15 2007